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<title>Tracking Damaps</title>
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<h2 align="center"><font color="#0000FF"><b>Symplectic representation using a 
generating function </b></font></h2>

<p align="center"><font color="#0000FF">(pioneered by Dragt and based here on 
Berz's dapin function)</font></p>

<p>Generally a <b><font color="#FF0000">canonical</font></b>&nbsp; DAMAP, i.e., 
a Taylor map centered around (0,0..,0.0) can be expressed as a generating 
function.<!--[if gte mso 9]> Consider the maps<![endif]--></p>
<p align="center"><img border="0" src="big_ta4.gif" width="623" height="55"></p>
<p align="left">and</p>
<p align="center"><img border="0" src="big_ta5.gif" width="623" height="55"></p>
<p>where z=(q,p).</p>
<p>The map (&nbsp; )<sup>1/ifac</sup><b> </b><font color="#FF0000">(<i>not always 
true for (1) </i>)</font> can often be expressed by a generating function of the 
form: </p>
<p align="center"><font size="6">&nbsp;
<img border="0" src="big_ta3.gif" width="301" height="103"></font></p>
<p>This is achieved by the<b>
<a href="../h_definition.htm#GENFIELD" style="text-decoration: none">type (genfield)</a>. </b></p>
<p>Equation (1) is selected the field<font color="#0000FF"> </font>
<font color="#FF0000">linear_in = .true.</font><font color="#0000FF"> </font>&nbsp;(default=.false.), 
otherwise equation (2) is used. Finally, the map used in the genfield is the 
ifac<sup>th</sup> root. </p>
<p><b><font size="4" color="#FF0000">An example of </font><font size="4">
<a href="../h_definition.htm#GENFIELD" style="text-decoration: none">type (genfield)</a><font color="#FF0000">
</font></font></b><font size="4">: the graphical results:</font></p>
<p align="center"><img border="0" src="gen.jpg" width="434" height="366"></p>
<p align="left">The red dots is the original Taylor map. The fat blue dots is 
the genfield type. Finally the yellow crosses shows the exact solution.</p>

<p align="center"><font color="#0000FF" size="5"><b>
<a href="../simple_programs/z_damaps_tracking_generating.f90">Program for this 
example</a></b></font></p>

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